1. ## inversed Z Transform

Hello!
I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

z/(z^2+z+1)

and

z^2/(z^2+z+1)

2. Originally Posted by inzaghina
Hello!
I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

z/(z^2+z+1)

and

z^2/(z^2+z+1)

You should probably factorize.
Also you may refer to Mathematica 7.0 - InverseZTransform.
As a little note, if $\displaystyle \lim\nolimits_{z\to\infty}F(z)/z\neq0$, then we can not find an exponentially bounded sequence $\displaystyle \{f(n)\}$ for which [tex]f(n)=Z^{-1}\{F(z)\}(n)[\math] holds.

3. Well, I have to do that by hand, not in the computer.
And I did a mistake, I have to solve Z^(-1) of :

z/(z^2+z+1)^2

and

z^2/(z^2+z+1)^2

have a good day!

4. Originally Posted by inzaghina
Hello!
I have a question,could you please give an idea about how can I calculate an inversed Z transform of these ( Z^(-1)[...] ) :

z/(z^2+z+1)
divide top and bottom by $\displaystyle z^2$ to get:

$\displaystyle \frac{z^{-1}}{z^{-2}+z^{-1}+1}$

then look this up in a table of inverse z-transforms (item 18 in the table in the Wikipedia article on the z-transform looks like what you need)

CB